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Transactions of the American Mathematical Society

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Completely unstable flows on $ 2$-manifolds


Author: Dean A. Neumann
Journal: Trans. Amer. Math. Soc. 225 (1977), 211-226
MSC: Primary 58F10
DOI: https://doi.org/10.1090/S0002-9947-1977-0448440-0
MathSciNet review: 0448440
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Abstract: Completely unstable flows on 2-manifolds are classified under both topological and $ {C^r}$-equivalence $ (1 \leqslant r \leqslant \infty )$, in terms of the corresponding orbit spaces.


References [Enhancements On Off] (What's this?)

  • [1] N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, Grundlehren math. Wiss., Band 161, Springer-Verlag, Berlin and New York, 1970. MR 44 #7077. MR 0289890 (44:7077)
  • [2] A. Haefliger and G. Reeb, Variétés (non séparées) à une dimension et structures feuilletées du plan, Enseignement Math. (2) 3 (1957), 107-125. MR 19, 671. MR 0089412 (19:671c)
  • [3] O. Hajek, Sections of dynamical systems in $ {E^2}$, Czechoslovak Math. J. 15 (90) (1965), 205-211. MR 31 #456. MR 0176181 (31:456)
  • [4] W. Kaplan, Regular curve-families filling the plane. I and II, Duke Math. J. 7 (1940), 154-185; ibid. 8 (1941), 11-46. MR 2, 322. MR 0004116 (2:322c)
  • [5] L. Markus, Parallel dynamical systems, Topology 8 (1969), 47-57. MR 38 #2806. MR 0234489 (38:2806)
  • [6] J. R. Munkres, Obstructions to the smoothing of piecewise-differentiable homeomorphisms, Ann. of Math. (2) 72 (1960), 521-554. MR 22 #12534. MR 0121804 (22:12534)
  • [7] D. A. Neumann, Smoothing continuous flows, J. Differential Equations (to appear). MR 0431280 (55:4281)
  • [8] T. Ważewski, Sur un problème de caractère intégral relatif à l'équation $ \partial z/\partial x + Q(x,y)\partial z/\partial y = 0$, Mathematica 8 (1934), 103-116.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0448440-0
Keywords: Flows on 2-manifolds, $ {C^r}$-equivalence of flows, orbit space
Article copyright: © Copyright 1977 American Mathematical Society

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